As you see from the above, we do have what we call Employment Insurance and it also covers more than just being unemployed, as it covers a maternity/paternity leave and it can also give you access to training funds . The number of months you work helps determine how many months you can be on EI . The amount you earn is the other part of the formula. Then we have slightly different formulas according to where in the country you worked, whether it was seasonal work, or fishing or farming .

From what I've heard from USA residents , the Canadian system is better than the USA one , BUT do check if your residency and citizenship status are factors that only a USA person might have to consider .

Yes, Canada has E.I. benefits: http://www.servicecanada.gc.ca/eng/sc/ei/index.shtml
But different categories of E.I. have different time limits.
For example,
"Maternity benefits are payable to the birth mother for a maximum of 15 weeks."
"Parental benefits are payable either to the biological or adoptive parents while they are caring for a newborn or adopted child, up to a maximum of 35 weeks."
Link - http://www.hrsdc.gc.ca/eng/workplaceskills/foreign_workers/ei_tfw/ceie_tfw.shtml

My understanding is that standard E.I. is payable for up to a maximum of 50 weeks.

Yes, we have that however in Canada it's called Employment Insurance. How many weeks you can claim and how much you get is dependent on how long you were at your last job and how much you made there.

As long as you are actively seeking employment, you can continue to receive E.I. benefits in some for or another. If you can't find a job and the Government places you in one, you have to accept it though.